On last week’s episode of Madam Secretary, the one-hour CBS drama about Washington, the normally level-headed American president goes crazy. He becomes enraged and bellicose, obsessed with American power and his own pride. He orders Russian satellites destroyed. He fires the secretary of defence for failing to obey his demented instructions.

After a few minutes, most of the audience (I imagine) begins to realize that this dotty imaginary figure, President Conrad Dalton (played by Keith Carradine), is based on the very real Donald Trump.

Dalton’s cabinet, meeting in secret, invokes the 25th amendment of the Constitution, which many people hope will happen to Trump. Dalton’s circle suspends his presidency and puts the vice-president in his place while he submits to a mental examination. Some in the cabinet are afraid they’ll be charged with staging a coup, but the secretary of state in the show’s title, Elizabeth McCord (Téa Leoni), believes this is the time for courage.

He is more at home in show business more than in politics

It turns out that President Dalton’s emotional trouble was caused by a benign brain tumour pushing on his frontal lobe, which the doctors can fix. Once diagnosed, he praises his cabinet as “true American heroes” putting “their country ahead of their personal relationship with me.” All episodes on Madame Secretary, no matter how complicated and dangerous, end happily. Even one, like this, titled “Sound and Fury.”

Watching this absorbing hour, I began to think of Donald Trump in a new way. It was right to place a Trump-like character at the centre of a TV episode. He’s more at home in show business than in politics. He’s become the American entertainer-in-chief. His words and deeds are so spectacularly strange that watching him feels like going to a circus.

He’s a star, and he knows it and enjoys it. He owes a lot to his stylist. That yellow comb-over gives him distinction, of a kind, without quite exaggerating him into a popinjay. No one mistakes him — “ever, ever,” as he would say — for anyone else, the first requirement for stardom.

Alec Baldwin plays U.S. President Donald Trump in an episode of Saturday Night Live on Feb. 4, 2017.Will Heath/NBC

His effect spreads through the cultural world. Thanks to Trump, Alec Baldwin’s flagging career has sprung to life in Baldwin’s dead-on Trumpian impression, from which Saturday Night Live has acquired a fresh credibility.

America’s greatest novelist, Philip Roth, who wrote a novel in which Charles Lindbergh becomes president, offered another comparison. He recently noted that Lindbergh, while a fascist, was also an authentic American hero because of his solo transatlantic flight at the age of 25. Whereas Trump is, by comparison, “a massive fraud, the evil sum of his deficiencies.” Roth added H.L. Mencken’s description of democracy as “the worship of jackals by jackasses.”

Trump’s effect reminds us we shouldn’t neglect the classics. He inspired the editor of The New Yorker, David Remnick, to quote Suetonius while comparing Trump to the Emperor Nero.

People can talk forever about what Trump said or didn't say

Those inspired by Trump also reach into modern popular art. Joe Scarborough on MSNBC’s Morning Joe combined Bob Dylan’s Nobel-winning Cold War poetry with current events, by predicting “a hard rain is going to fall on Donald Trump and the Republicans.”

People can talk forever about what Trump said or didn’t say, making Michael Wolff’s Fire and Fury an instant bestseller. It’s just as amusing to read the reports of those who were in the room when he gave his opinion of certain African countries. It’s also entertaining to read about journalists all over the world trying desperately to translate “shithole.” An Israeli reporter said it’s much more poetic in Hebrew.

Accidentally or not, Trump teaches us the charm and beauty of irony. His cognition test result provides the perfect example. Last week the White House announced that his annual medical examination included a test of mental aptitude. He passed it like a champion, scoring 30 out of 30 possible points. It didn’t exactly prove his claim to be a “stable genius,” but it was reassuring.

And, ironically, proof of his mental ability came from a test written many years ago by a Lebanese-born neurologist who happens to be an immigrant to Canada. Two decades ago, Ziad Nasreddine designed the Montreal Cognitive Assessment to judge whether a patient has suffered light cognitive impairment or is experiencing the onset of Alzheimer’s disease. (This test is the one where you draw a clock and identify a drawing of a camel.) It’s been used in 200 countries, in 60 languages.

Nasreddine says he hopes the president draws some lessons from his story. “I’m an immigrant. I think immigrants can be proud that they are contributing. And this is a good example, I think, that will be helpful to change views about immigration, and maybe for Mr. Trump himself to consider immigrants as contributors to advancing science, advancing our societies.”